Three-step  and four-step random walk integrals

Borwein, Jonathan M.; Straub, Armin; Wan, James

Three-step and four-step random walk integrals

journal contribution

posted on 2025-05-09, 07:55 authored by Jonathan M. Borwein, Armin Straub, James Wan

We investigate the moments of 3-step and 4-step uniform random walk in the plane. In particular, we further analyse a formula conjectured in BNSW expressing 4-step moments in terms of 3-step moments. Diverse related results including hypergeometric and elliptic closed forms for W₄(± 1) are given and two new conjectures are recorded.

History

Journal title

Experimental Mathematics

Volume

22

Issue

1

Pagination

1-14

Publisher

Taylor & Francis

Language

en, English

College/Research Centre

Faculty of Engineering and Built Environment

Rights statement

This is an electronic version of an article published in Experimental Mathematics Vol. 22, Issue 1, p. 1-14. Experimental Mathematics is available online at: http://www.tandfonline.com/openurl?genre=article&issn=1058-6458&volume=22&issue=1&spage=1

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Keywords

random walks hypergeometric functions Meijer G-functions elliptic integrals